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On fuzzy soft semi-pre-open sets and fuzzy soft semi-pre-continuous mappings

Year 2017, Volume: 46 Issue: 5, 851 - 863, 01.10.2017

Abstract

The main aim of this paper is to initiate and explore the properties of fuzzy soft semi-pre-open(closed) sets. We introduce and investigate fuzzy soft semi-pre-interior and fuzzy soft semi-pre-closure in fuzzy soft topological spaces. Moreover, we dene and study the characterizations of fuzzy soft semi-pre-continuous and fuzzy soft semi-pre-open(closed) mappings in fuzzy soft topological spaces.

References

  • B. Ahmad, S. Hussain : On some structures of soft topology, Mathematical Sciences, 6(64) (2012), 7 Pages.
  • B. Ahmad, A. Kharal: Mappings on fuzzy soft classes, Advances in Fuzzy Systems, (2009), Article ID 407890, 6 Pages.
  • H. Aktas, N. Cagman: Soft sets and soft groups, Information Sciences , 177(13)(2007), 27262735.
  • M. I. Ali, F. Feng, X. Liu, W. K. Min, and M. Shabir: On some new operations in soft set theory, Computers and Mathematics with Applications, 57(9)(2009),1547-1553.
  • C. L. Chang: Fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 24(1)(1968), 182-190.
  • B. Chen: Soft semi-open sets and related properties in soft topological spaces, Applied Mathematics Information Sciences, 7(1)(2013), 287-294.
  • B. Chen: Soft local properties of soft semi-open sets, Discrete Dynamics in Nature and Society, Vol. 2013, Article ID 298032, 6 pages.
  • S. Du, Q. Qin, Q. Wang, and B. Li: Fuzzy description of topological relations I: a unied fuzzy 9-intersection model, Proceedings of the 1st International Conference on Advances in Natural Computation (ICNC 05), vol. 3612 of Lecture Notes in Computer Science, pp. 1261-1273, Changsha, China, August 2005.
  • M. J. Egenhofer and R. D. Franzosa: Point-set topological spatial relations, International Journal of Geographical Information Systems, 5(2)(1991), 161-174.
  • M. J. Egenhofer and J. Herring: Categorizing binary topological relations between regions, lines and points in geographic databases, Tech. Rep., Department of Surveying Engineering, University of Maine, Orono, Me, USA, 1991.
  • F. Feng, Y. B. Jun, X. Zhao: Soft semi rings,Computers and Mathematics with Applica- tions, 56(10)(2008), 2621-2628.
  • F. Feng, Y. M. Li: Soft subsets and soft product operations, Information Sciences, 232(2013), 44-57.
  • F. Feng, Y. M. Li, N. Cagman: Generalized uni-int decision making scheme based on choice value soft sets, Europeon Journal of Operaion Research, 220(2012), 162-170.
  • F. Feng, M. Akram, B. Davvaz, V. Leoreanu-Fotea: Attribute analysis of information systems based on elementry soft implications, Knowledge Based Systems, 70(2014),281 292.
  • F. Feng, W. Pedrycz: On scalar products and decomposition theorems of fuzzy soft sets, Journal of Multi-valued Logic and Soft Computing, 25(2015), 45-80.
  • C. Gundaz, S. Bayramov: Some results on fuzzy soft topological spaces, Mathematical Problems in Engineering, (2013), Article ID 935308, 10 Pages.
  • S. Hussain, B. Ahmad : Some properties of soft topological spaces, Computers and Mathe- matics with Applications, 62(11) (2011) 4058-4067.
  • S. Hussain, B. Ahmad : Soft separation axioms in soft topological spaces, Hacettepe Journal of Mathematics and Statistics, 44(3) (2015), 559-568.
  • S. Hussain: A note on soft connectedness, Journal of Egyptian Mathematical Society, 23(1) (2015), 6-11.
  • S. Hussain: On some soft functions, Mathematical Science Letters, 4(1) (2015), 55-61.
  • S. Hussain: Properties of soft semi-open and soft semi-closed sets, Pensee Journal, 76(2)(2014), 133-143.
  • S. Hussain: On some generalized structures in fuzzy soft topological spaces, Information Science Letters, 4(3)(2015), 107-115.
  • S. Hussain: On weak and strong forms of fuzzy soft open sets, Fuzzy Information and Engineering, (8)(2016), 451-463.
  • A. Z. Khameneh, A. Kilicman and A. R. Salleh: Fuzzy soft boundary, Annals of Fuzzy Mathematics and Informatics, 8(5)(2014), 687-703.
  • Z. Kong, L. Gao, L. Wong, S. Li: The normal parameter reduction of soft sets and its algorithm, J. Comp. Appl. Math., 21 (2008), 941-945.
  • B. Kostek: Soft set approach to subjective assesment of sound quality , Fuzzy Systems Proceeding, 1998, IEEE World Congress on Computational Intelligence, 4-9 May, 669- 674, 1998, DOI: 10.1109/FUZZY.1998.687568.
  • P. K. Maji, R. Biswas, A. R. Roy: Soft set theory, Computers and Mathematics with Applications, 45(4-5) (2003), 555-562.
  • P . K. Maji, R. Biswas, A. R. Roy: An application of soft sets in a decision making problem, Computers and Mathematics with Applications, 44(8-9) (2002), 1077-1083.
  • P. K. Maji, R. Biswas, A. R. Roy: Fuzzy soft sets, J. Fuzzy Math., 9(3)(2001), 589-602.
  • W. K. Min: Soft sets over a common topological universe, Jouranl of Intelligent and Fuzzy Systems, 26:2099(2014).
  • D. Molodtsov: Soft set theory rst results, Computers and Mathematics with Applications, 37(4-5) (1999), 19-31.
  • D. Molodtsov, V.Y. Leonov, D.V. Kovkov: Soft sets technique and its application, Nechetkie Sistemy i Myagkie Vychisleniya, 9(1)(2006), 28-39.
  • M. Mushrif, S. Sengupta, A. K. Ray: Texture classication using a novel, soft set theory based classication algorithm, Springer Berlin, Heidelberg , 254-264(2006).
  • G. J. Nazaro: Fuzzy topological polysystems, Journal of Mathematical Analysis and Ap- plications, 41(1973),734-742.
  • D. Pie, D. Miao: From soft sets to information systems, X. Hu, Q. Liu, A. Skowron, Y. Y. Lin, R. R. Yager, B. Zhang(Eds.) Proceedings of Granular Computing Vol. 2, IEEE(2005), 2005, 617-621.
  • M. Shabir, M. Naz: On soft topological spaces, Computers and Mathematics with Applica- tions, 61(7)(2011), 1786-1799.
  • B. Tanay and M. B. Kandemir: Topological structure of fuzzy soft sets, Computers and Mathematics with Applications, 61(10)(2011), 2952-2957.
  • B. P. Varol and H. Aygun: Fuzzy soft topology, Hacettepe Journal of Mathematics and Statistics, 41(3)(2012), 407-419.
  • Z. Xio, L. Chen, B. Zhong, S. Ye: Recognition for information based on the theory of soft sets, J. Chen(Ed.), Procedding of ICSSSM-05, IEEE(2005), (2)(2005), 1104-1106.
  • L. A. Zadeh: Fuzzy sets, Information and Control, 8(1996), 338-353.
  • I. Zorlutana, N. Akdag, W. K. Min: Remarks on soft topological spaces, Annals of fuzzy Mathematics and Informatics, 3(2)(2012),171-185.
Year 2017, Volume: 46 Issue: 5, 851 - 863, 01.10.2017

Abstract

References

  • B. Ahmad, S. Hussain : On some structures of soft topology, Mathematical Sciences, 6(64) (2012), 7 Pages.
  • B. Ahmad, A. Kharal: Mappings on fuzzy soft classes, Advances in Fuzzy Systems, (2009), Article ID 407890, 6 Pages.
  • H. Aktas, N. Cagman: Soft sets and soft groups, Information Sciences , 177(13)(2007), 27262735.
  • M. I. Ali, F. Feng, X. Liu, W. K. Min, and M. Shabir: On some new operations in soft set theory, Computers and Mathematics with Applications, 57(9)(2009),1547-1553.
  • C. L. Chang: Fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 24(1)(1968), 182-190.
  • B. Chen: Soft semi-open sets and related properties in soft topological spaces, Applied Mathematics Information Sciences, 7(1)(2013), 287-294.
  • B. Chen: Soft local properties of soft semi-open sets, Discrete Dynamics in Nature and Society, Vol. 2013, Article ID 298032, 6 pages.
  • S. Du, Q. Qin, Q. Wang, and B. Li: Fuzzy description of topological relations I: a unied fuzzy 9-intersection model, Proceedings of the 1st International Conference on Advances in Natural Computation (ICNC 05), vol. 3612 of Lecture Notes in Computer Science, pp. 1261-1273, Changsha, China, August 2005.
  • M. J. Egenhofer and R. D. Franzosa: Point-set topological spatial relations, International Journal of Geographical Information Systems, 5(2)(1991), 161-174.
  • M. J. Egenhofer and J. Herring: Categorizing binary topological relations between regions, lines and points in geographic databases, Tech. Rep., Department of Surveying Engineering, University of Maine, Orono, Me, USA, 1991.
  • F. Feng, Y. B. Jun, X. Zhao: Soft semi rings,Computers and Mathematics with Applica- tions, 56(10)(2008), 2621-2628.
  • F. Feng, Y. M. Li: Soft subsets and soft product operations, Information Sciences, 232(2013), 44-57.
  • F. Feng, Y. M. Li, N. Cagman: Generalized uni-int decision making scheme based on choice value soft sets, Europeon Journal of Operaion Research, 220(2012), 162-170.
  • F. Feng, M. Akram, B. Davvaz, V. Leoreanu-Fotea: Attribute analysis of information systems based on elementry soft implications, Knowledge Based Systems, 70(2014),281 292.
  • F. Feng, W. Pedrycz: On scalar products and decomposition theorems of fuzzy soft sets, Journal of Multi-valued Logic and Soft Computing, 25(2015), 45-80.
  • C. Gundaz, S. Bayramov: Some results on fuzzy soft topological spaces, Mathematical Problems in Engineering, (2013), Article ID 935308, 10 Pages.
  • S. Hussain, B. Ahmad : Some properties of soft topological spaces, Computers and Mathe- matics with Applications, 62(11) (2011) 4058-4067.
  • S. Hussain, B. Ahmad : Soft separation axioms in soft topological spaces, Hacettepe Journal of Mathematics and Statistics, 44(3) (2015), 559-568.
  • S. Hussain: A note on soft connectedness, Journal of Egyptian Mathematical Society, 23(1) (2015), 6-11.
  • S. Hussain: On some soft functions, Mathematical Science Letters, 4(1) (2015), 55-61.
  • S. Hussain: Properties of soft semi-open and soft semi-closed sets, Pensee Journal, 76(2)(2014), 133-143.
  • S. Hussain: On some generalized structures in fuzzy soft topological spaces, Information Science Letters, 4(3)(2015), 107-115.
  • S. Hussain: On weak and strong forms of fuzzy soft open sets, Fuzzy Information and Engineering, (8)(2016), 451-463.
  • A. Z. Khameneh, A. Kilicman and A. R. Salleh: Fuzzy soft boundary, Annals of Fuzzy Mathematics and Informatics, 8(5)(2014), 687-703.
  • Z. Kong, L. Gao, L. Wong, S. Li: The normal parameter reduction of soft sets and its algorithm, J. Comp. Appl. Math., 21 (2008), 941-945.
  • B. Kostek: Soft set approach to subjective assesment of sound quality , Fuzzy Systems Proceeding, 1998, IEEE World Congress on Computational Intelligence, 4-9 May, 669- 674, 1998, DOI: 10.1109/FUZZY.1998.687568.
  • P. K. Maji, R. Biswas, A. R. Roy: Soft set theory, Computers and Mathematics with Applications, 45(4-5) (2003), 555-562.
  • P . K. Maji, R. Biswas, A. R. Roy: An application of soft sets in a decision making problem, Computers and Mathematics with Applications, 44(8-9) (2002), 1077-1083.
  • P. K. Maji, R. Biswas, A. R. Roy: Fuzzy soft sets, J. Fuzzy Math., 9(3)(2001), 589-602.
  • W. K. Min: Soft sets over a common topological universe, Jouranl of Intelligent and Fuzzy Systems, 26:2099(2014).
  • D. Molodtsov: Soft set theory rst results, Computers and Mathematics with Applications, 37(4-5) (1999), 19-31.
  • D. Molodtsov, V.Y. Leonov, D.V. Kovkov: Soft sets technique and its application, Nechetkie Sistemy i Myagkie Vychisleniya, 9(1)(2006), 28-39.
  • M. Mushrif, S. Sengupta, A. K. Ray: Texture classication using a novel, soft set theory based classication algorithm, Springer Berlin, Heidelberg , 254-264(2006).
  • G. J. Nazaro: Fuzzy topological polysystems, Journal of Mathematical Analysis and Ap- plications, 41(1973),734-742.
  • D. Pie, D. Miao: From soft sets to information systems, X. Hu, Q. Liu, A. Skowron, Y. Y. Lin, R. R. Yager, B. Zhang(Eds.) Proceedings of Granular Computing Vol. 2, IEEE(2005), 2005, 617-621.
  • M. Shabir, M. Naz: On soft topological spaces, Computers and Mathematics with Applica- tions, 61(7)(2011), 1786-1799.
  • B. Tanay and M. B. Kandemir: Topological structure of fuzzy soft sets, Computers and Mathematics with Applications, 61(10)(2011), 2952-2957.
  • B. P. Varol and H. Aygun: Fuzzy soft topology, Hacettepe Journal of Mathematics and Statistics, 41(3)(2012), 407-419.
  • Z. Xio, L. Chen, B. Zhong, S. Ye: Recognition for information based on the theory of soft sets, J. Chen(Ed.), Procedding of ICSSSM-05, IEEE(2005), (2)(2005), 1104-1106.
  • L. A. Zadeh: Fuzzy sets, Information and Control, 8(1996), 338-353.
  • I. Zorlutana, N. Akdag, W. K. Min: Remarks on soft topological spaces, Annals of fuzzy Mathematics and Informatics, 3(2)(2012),171-185.
There are 41 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Sabir Hussain This is me

Publication Date October 1, 2017
Published in Issue Year 2017 Volume: 46 Issue: 5

Cite

APA Hussain, S. (2017). On fuzzy soft semi-pre-open sets and fuzzy soft semi-pre-continuous mappings. Hacettepe Journal of Mathematics and Statistics, 46(5), 851-863.
AMA Hussain S. On fuzzy soft semi-pre-open sets and fuzzy soft semi-pre-continuous mappings. Hacettepe Journal of Mathematics and Statistics. October 2017;46(5):851-863.
Chicago Hussain, Sabir. “On Fuzzy Soft Semi-Pre-Open Sets and Fuzzy Soft Semi-Pre-Continuous Mappings”. Hacettepe Journal of Mathematics and Statistics 46, no. 5 (October 2017): 851-63.
EndNote Hussain S (October 1, 2017) On fuzzy soft semi-pre-open sets and fuzzy soft semi-pre-continuous mappings. Hacettepe Journal of Mathematics and Statistics 46 5 851–863.
IEEE S. Hussain, “On fuzzy soft semi-pre-open sets and fuzzy soft semi-pre-continuous mappings”, Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 5, pp. 851–863, 2017.
ISNAD Hussain, Sabir. “On Fuzzy Soft Semi-Pre-Open Sets and Fuzzy Soft Semi-Pre-Continuous Mappings”. Hacettepe Journal of Mathematics and Statistics 46/5 (October 2017), 851-863.
JAMA Hussain S. On fuzzy soft semi-pre-open sets and fuzzy soft semi-pre-continuous mappings. Hacettepe Journal of Mathematics and Statistics. 2017;46:851–863.
MLA Hussain, Sabir. “On Fuzzy Soft Semi-Pre-Open Sets and Fuzzy Soft Semi-Pre-Continuous Mappings”. Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 5, 2017, pp. 851-63.
Vancouver Hussain S. On fuzzy soft semi-pre-open sets and fuzzy soft semi-pre-continuous mappings. Hacettepe Journal of Mathematics and Statistics. 2017;46(5):851-63.